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If-f-x-x-1-2-1-2-find-dy-dx-




Question Number 97784 by 175 last updated on 09/Jun/20
If f(x)=((( x)^(1/2) )^(1/2) )^ā‹°   find: (dy/dx)
$${If}\:{f}\left({x}\right)=\left(\left(\left(\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\iddots} \\ $$$${find}:\:\frac{{dy}}{{dx}} \\ $$
Answered by mr W last updated on 09/Jun/20
f(x)=lim_(nā†’āˆž) x^(((1/2))^n ) =x^0 =1  (dy/dx)=0
$${f}\left({x}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}{x}^{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}} } ={x}^{\mathrm{0}} =\mathrm{1} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{0} \\ $$

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